QUADRATIC FUNCTIONS

Lessons & Objectives:

Introduction to Quadratic Functions

• Evaluate a quadratic function using tables, graphs, and equations.

• Identify a quadratic function and the values of the coefficients and constant from the standard form.

• Calculate the rate of change of a quadratic function over an interval of its domain, and compare it to linear and exponential functions.

Quadratic Functions: Standard Form

• Graph a quadratic function given in standard form, identifying the key features of the graph.

Quadratic Functions: Factored Form

• Graph a quadratic function given in factored form, identifying the key features of the graph.

Quadratic Functions: Vertex Form

• Relate the parameters of a quadratic function in vertex form to transformations of the graph y = x2 .

• Graph a quadratic function given in vertex form, identifying the key features of the graph.

Completing the Square

• Relate the parameters of a quadratic function in vertex form to transformations of the graph y = x2 .

• Determine key aspects of the graph of a quadratic function given in standard form and with a = 1 by writing it in vertex form.

• Write quadratic functions given in standard form and with a = 1 into vertex form by completing the square.

• Relate the geometric model of completing the square to the algebraic process.

Completing the Square (Continued)

• Write quadratic functions given in standard form into vertex form by completing the square.

• Determine key aspects of the graph of a quadratic function given in standard form by writing it in vertex form.

• Relate the parameters of a quadratic function in vertex form to transformations of the graph y = x2 .

Modeling with Quadratic Functions

• Use quadratic functions to solve mathematical and real-world problems.

• Write quadratic functions to model problems.